Question

2. Dataset B consists of the values {10,12,14,24,25,27,28,30,30,32,33,33,34,37,38,38,40,41,43,

44,44,46,47,49,56,58}.

(a) What is the median of Dataset B?

(b) To one decimal, what is the sample standard deviation of Dataset B? (Don’t calculate this out by hand.)

(c) Make a table of the frequency distribution (not the relative frequency distribution) of Dataset B, using the intervals 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. Be sure to appropriately label the table headings.

(d) Make a graph of the relative frequency distribution (not the frequency distribution) of Dataset B, using the intervals 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. Be sure to appropriately label the horizontal and vertical axes.

Answer 1

Part A

Median Calculation

In order to compute the median, the data needs to be put into ascending order, as shown in the table below

Position	X (Asc. Order)
1	10
2	12
3	14
4	24
5	25
6	27
7	28
8	30
9	30
10	32
11	33
12	33
13	34
14	37
15	38
16	38
17	40
18	41
19	43
20	44
21	44
22	46
23	47
24	49
25	56
26	58

Since the sample size n=26 is even, we have that (n+1)/2=(26+1)/2=13.5 is not an integer value, the median is computing by taking the average of the values at the positions 13th and 14th, as shown below

Part B

The sample size is n = 26n=26. The provided sample data along with the data required to compute the sample mean \bar XXˉ and sample variance s^2s2 are shown in the table below:

	X	X2
	10	100
	12	144
	14	196
	24	576
	25	625
	27	729
	28	784
	30	900
	30	900
	32	1024
	33	1089
	33	1089
	34	1156
	37	1369
	38	1444
	38	1444
	40	1600
	41	1681
	43	1849
	44	1936
	44	1936
	46	2116
	47	2209
	49	2401
	56	3136
	58	3364
Sum =	913	35797

The sample variance s² is

Therefore, the sample standard deviation s is

Part C

Frequency Distribtuion table

Lower Class	Upper Class	Values	Frequency
10	19	10,12,14	3
20	29	24,25,27,28	4
30	39	30,30,32,33,33,34,37,38,38	9
40	49	40,41,43,44,44,46,47,49	8
50	59	56,58	2

Class Interval	Frequency
10-19	3
20-29	4
30-39	9
40-49	8
50-59	2
Total	26

Part D

Class Interval	Frequency	Relative Frequency Distribution
10-19	3	3/26 = 01154
20-29	4	4/26 = 0.1538
30-39	9	9/26 = 0.3461
40-49	8	8/26 = 0.3077
50-59	2	2/26 = 0.770
Total	26	1

Graph